Edexcel 2020 Pure Maths Paper 2 9MA0/02

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Edexcel 2020 Pure Maths Paper 2 Question Paper (pdf)

Edexcel 2020 Pure Maths Paper 2 Mark Scheme (pdf)

  1. The table below shows corresponding values of x and y for y =
    The values of y are given to 4 significant figures.
    (a) Use the trapezium rule, with all the values of y in the table, to find an estimate for giving your answer to 3 significant figures.
  2. Relative to a fixed origin, points P, Q and R have position vectors p, q and r respectively.
    Given that
  • P, Q and R lie on a straight line
  • Q lies one third of the way from P to R
    show that q = 1/3(r + 2p)
  1. (a) Given that
    2log (4 − x) = log(x + 8)
    show that
    x2 − 9x + 8 = 0
    (b) (i) Write down the roots of the equation
    x2 − 9x + 8 = 0
    (ii) State which of the roots in (b)(i) is not a solution of
    2log(4 − x) = log(x + 8)
    giving a reason for your answer.

  1. In the binomial expansion of
    (a + 2x)7
    where a is a constant
    the coefficient of x4 is 15 120
    Find the value of a.
  2. The curve with equation y = 3 × 2x
    meets the curve with equation y = 15 − 2x+1 at the point P.
    Find, using algebra, the exact x coordinate of P.
  3. (a) Given that
    find the values of the constants A, B and C
  4. Figure 1 shows a sketch of the curve C with equation
  5. A curve C has equation y = f(x)
    Given that
  • fʹ(x) = 6x2 + ax − 23 where a is a constant
  • the y intercept of C is −12
  • (x + 4) is a factor of f(x) find, in simplest form, f(x)
  1. A quantity of ethanol was heated until it reached boiling point.
    The temperature of the ethanol, θ °C, at time t seconds after heating began, is modelled by the equation
    θ = A − Be−0.07t
    where A and B are positive constants.
    Given that
  • the initial temperature of the ethanol was 18°C
  • after 10 seconds the temperature of the ethanol was 44°C
    (a) find a complete equation for the model, giving the values of A and B to 3 significant figures.
    Ethanol has a boiling point of approximately 78°C
    (b) Use this information to evaluate the model.
  1. (a) Show that
    cos 3A ≡ 4cos3 A − 3 cosA
    (b) Hence solve, for −90°  x  180°, the equation
    1 − cos3x = sin2 x
  2. Figure 2 shows a sketch of the graph with equation
    y = 2 | x + 4| − 5
    The vertex of the graph is at the point P, shown in Figure 2.
    (a) Find the coordinates of P.
    (b) Solve the equation
    3x + 40 = 2 | x + 4| − 5
    A line l has equation y = ax, where a is a constant.
    Given that l intersects y = 2| x + 4| − 5 at least once,
    (c) find the range of possible values of a, writing your answer in set notation.
  3. The curve shown in Figure 3 has parametric equations
    x = 6sint y = 5 sin 2t 0  t  π/2
    The region R, shown shaded in Figure 3, is bounded by the curve and the x-axis.
  4. The function g is defined by
  5. A circle C with radius r
  • lies only in the 1st quadrant
  • touches the x-axis and touches the y-axis
    The line l has equation 2x + y = 12
    (a) Show that the x coordinates of the points of intersection of l with C satisfy
    5x2 + (2r − 48) x + (r2 − 24r + 144) = 0
    Given also that l is a tangent to C,
    (b) find the two possible values of r, giving your answers as fully simplified surds.
  1. A geometric series has common ratio r and first term a.
    Given r ≠ 1 and a ≠ 0
    (a) prove that

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